• Values, variables
• Vectors
• Matrices
• Loops
• Logical statements
• Control statements
• Functions

• Compute the mean with your own function
• Evolution in action: fast and slow sloths -> exercise session
• Append and lists -> exercise session

# Vectors
some_numbers <- c(30, 50, 60)

some_numbers[c(2,3)]
some_numbers > 3
some_numbers * 5

What is total_sum?

numbers <- 1:4
total_sum <- 0
n <- length(numbers)

# start loop
for (i in 1:n) {
  
  if(i %% 2 == 0){
     total_sum <- total_sum + numbers[i]
  } else {
    total_sum <- total_sum + 2*numbers[i]
  }

}

Microprocessors can only represent two signs (states):

• ‘Off’ = 0
• ‘On’ = 1

• Only two signs: 0, 1.
• Base 2.
• Columns: \(2^0=1\), \(2^1=2\), \(2^2=4\), and so forth.

What is the decimal number 139 in the binary counting frame?

What is the decimal number 139 in the binary counting frame?

• Solution:

\[(1 \times 2^7) + (1 \times 2^3) + (1 \times 2^1) + (1 \times 2^0) = 139.\]

What is the decimal number 139 in the binary counting frame?

• Solution:

\[(1 \times 2^7) + (1 \times 2^3) + (1 \times 2^1) + (1 \times 2^0) = 139.\]

• More precisely:

\[(1 \times 2^7) + (0 \times 2^6) + (0 \times 2^5) + (0 \times 2^4) + (1 \times 2^3)\\ + (0 \times 2^2) + (1 \times 2^1) + (1 \times 2^0) = 139.\]

• That is, the number 139 in the decimal system corresponds to 10001011 in the binary system.

• Sufficient to represent all natural numbers in the decimal system.

• Sufficient to represent all natural numbers in the decimal system.
• Representing fractions is tricky
  • e.g. \(1/3=0.333..\) actually constitutes an infinite sequence of 0s and 1s.
  • Solution: ‘floating point numbers’ (not 100% accurate)

# Subtracting two nearly identical floating-point numbers
x <- 0.3 - 0.2
y <- 0.1

# Check if they are equal
result <- x == y

print(x)       

## [1] 0.1

print(y)       

## [1] 0.1

print(result)  

## [1] FALSE

print(format(x, digits = 20))  # prints a more precise value of x

## [1] "0.099999999999999977796"

print(format(y, digits = 20))  # prints a more precise value of y

## [1] "0.10000000000000000555"

tolerance <- 1e-9
equal <- abs(x - y) < tolerance
print(equal)

## [1] TRUE

If computers only understand 0 and 1, how can they express decimal numbers like 139?

If computers only understand 0 and 1, how can they express decimal numbers like 139?

• Standards define how symbols, colors, etc are shown on the screen.
• Facilitates interaction with a computer (our keyboards do not only consist of a 0/1 switch).

• Binary numbers can become quite long rather quickly.
• Computer Science: refer to binary numbers with the hexadecimal system.

• 16 symbols:
  • 0-9 (used like in the decimal system)…
  • and A-F (for the numbers 10 to 15).

• 16 symbols:
  • 0-9 (used like in the decimal system)…
  • and A-F (for the numbers 10 to 15).
• 16 symbols >>> base 16: each digit represents an increasing power of 16 (\(16^{0}\), \(16^{1}\), etc.).

What is the decimal number 139 expressed in the hexadecimal system?

What is the decimal number 139 expressed in the hexadecimal system?

• Solution: \[(8\times 16^1) + (11\times 16^0) = 139.\]

• More precisely: \[(8\times 16^1) + (B\times 16^0) = 8B = 139.\]

• Hence: 10001011 (in binary) = 8B (in hexadecimal) = 139 in decimal.

Advantages (when working with binary numbers)

1. Shorter than raw binary representation
2. Much easier to translate forth and back between binary and hexadecimal than binary and decimal.

How can a computer understand text if it only understands 0s and 1s?

A modified version of South Korean Dubeolsik (two-set type) for old hangul letters. (Illustration by Yes0song 2010, Creative Commons Attribution-Share Alike 3.0 Unported)

How can a computer understand text if it only understands 0s and 1s?

• Standards define how 0s and 1s correspond to specific letters/characters of different human languages.
• These standards are usually called character encodings.
• Coded character sets that map unique numbers (in the end in binary coded values) to each character in the set.

How can a computer understand text if it only understands 0s and 1s?

• Standards define how 0s and 1s correspond to specific letters/characters of different human languages.
• These standards are usually called character encodings.
• Coded character sets that map unique numbers (in the end in binary coded values) to each character in the set.
• For example, ASCII (American Standard Code for Information Interchange), now superseded by utf-8 (Unicode).

ASCII logo. (public domain).

• In practice, Data Science means handling digital data of all formats and shapes.
  • Diverse sources.
  • Different standards.
  • Different languages (Japanese vs English).
  • read/store data.
• At the lowest level, this means understanding/handling encodings.

Two core themes of this course:

1. How can data be stored digitally and be read by/imported to a computer?
2. How can we give instructions to a computer by writing computer code?

Two core themes of this course:

1. How can data be stored digitally and be read by/imported to a computer?
2. How can we give instructions to a computer by writing computer code?

In both of these domains we mainly work with one simple type of document: text files.

• A collection of characters stored in a designated part of the computer memory/hard drive.
• An easy-to-read representation of the underlying information (0s and 1s)!

• A collection of characters stored in a designated part of the computer memory/hard drive.
• An easy to read representation of the underlying information (0s and 1s)!
• Common device to store data:
  • Structured data (tables)
  • Semi-structured data (websites)
  • Unstructured data (plain text)
• Typical device to store computer code.

Install RStudio from here!

Install Atom from here!

Install VScode from here!

Install Sublime text from here!

• R runs on one CPU core by default.
• All modern CPUs have multiple cores.
• Advanced: explore parallelization with plyr, doParallel() and future

large_matrix <- matrix(1, nrow=1e8, ncol=1e8)

## Error in matrix(1, nrow = 1e+08, ncol = 1e+08): Vektor ist zu groß

• Try to create a matrix with \(10^8 \times 10^8\) elements.
• Assuming each number is stored using 8 bytes, this matrix would require \(8\times10^16\) bytes of RAM (more on bytes in the next lecture).

Recall the initial example (survey) of this course.

1. Access a website (over the Internet), use keyboard to enter data into a website (a Google sheet in that case).

2. R program accesses the data of the Google sheet (again over the Internet), downloads the data, and loads it into RAM.

3. Data processing: produce output (in the form of statistics/plots), output on screen.